Combining graph embedding and sparse regression with structure low-rank representation for semi-supervised learning

Abstract

In this paper, we propose a novel method for semi-supervised learning by combining graph embedding and sparse regression, termed as graph embedding and sparse regression with structure low rank representation (GESR-LR), in which the embedding learning and the sparse regression are performed in a combined approach. Most of the graph based semi-supervised learning methods take into account the local neighborhood information while ignoring the global structure of the data. The proposed GESR-LR method learns a low-rank weight matrix by projecting the data onto a low-dimensional subspace. The GESR-LR makes full use of the supervised learning information in the construction of the affinity matrix, and the affinity construction is combined with graph embedding in a single step to guarantee the global optimal solution. In the dimensionality reduction procedure, the proposed GESR-LR can preserve the global structure of the data, and the learned low-rank weight matrix can effectively reduce the influence of the noise. An effective novel algorithm to solve the corresponding optimization problem was designed and is presented in this paper. Extensive experimental results demonstrate that the GESR-LR method can obtain a higher classification accuracy than other state-of-the-art methods.